Half-space theorems for minimal surfaces in Nil_3 and Sol_3

We prove some half-space theorems for minimal surfaces in the Heisenberg group Nil_3 and the Lie group Sol_3 endowed with their left-invariant Riemannian metrics. If S is a properly immersed minimal surface in Nil_3 that lies on one side of some entire minimal graph G, then S is the image of G by a vertical translation. If S is a properly immersed minimal surface in Sol_3 that lies on one side of a special plane, then S is another special plane.Comment: 19 pages, 3 figure

Carbon-13 nuclear magnetic resonance spectra and mechanism of bridge–terminal carbonyl exchange in di-µ-carbonyl-bis[carbonyl(η-cyclopentadienyl)iron](Fe–Fe)[{(η-C5H5)Fe(CO)2}2]; cd-di-µ-carbonyl-f-carbonyl-ae-di(η-cyclopentadienyl)-b-(triethyl -phosphite)di-iron(Fe–Fe)[(η-C5H5)2Fe2(CO)3P(OEt)3], and some related complexes

A mechanism involving carbonyl-bridge breaking, rotation about the Fe–Fe bond, and bridge reformation is shown to account qualitatively for changes in the carbonyl region of the 13C n.m.r spectrum of the complex [(cp)(OC)[graphic omitted]e(cp){P(OEt)3}] and quantitatively for [(cp)(OC)[graphic omitted]e(CO)(cp)](cp =η-cyclopentadienyl).The activation energy for this process, 49.0 ± 4 kJ mol^–1(11.7 ± 1 kcal mol^–1), is close to that reported for cis–trans-isomerization of the cp groups, in accord with this mechanism. Variable-temperature 13C n.m.r. spectra of the complexes [(cp)(OC)[graphic omitted]u(CO)(cp)] and [(cp)(OC)[graphic omitted]i(cp)] are also reported

Indeterminate Architecture: Scissor-Pair Transformable Structures

Most traditional approaches to architectural design assume that the analysis of present situations and the prediction of future ones will offer unique answers that would ultimately define correct and unique architectural solutions. However, this approach is based on two questionable believes: First, that present situations are representative of a reality to be produced in the future, and, second, that these situations are fixed and invariable throughout time.The vision here is that an alternative approach is needed: a method that assumes and uses the uncertainties about present and future situations through the design of indeterminate solutions. Instead of analysing present and predicting future situations, designers should envision transformable environments able to offer a range of alternatives to be defined and redefined by the users in real-time – an indeterminate architecture, sympathetic to uncertainty, incompleteness and emergent situations that can neither be analysed nor predicted beforehand.This paper addresses the design of an indeterminate architecture, through proposing two main directions: Designing the Range and Enabling the Choice. While the former refers to transformable solutions able to offer a variety of states, the later refers to the selection of states by the user, within that range according to chance and emergent situations.The structure of this paper is organised around these two ideas by presenting an architectural background, some technical methods, and an empirical experiment. While the theoretical background investigates the original ideas and project about indeterminacy within an architectural framework, the technical methods analyse the range of states within the transformation of scissor-pair transformable structures, and study the real-time control and interaction within artificial intelligence (AI) robotic solutions. The empirical experiment uses the architectural background and the technical methods to materialise and radicalise indeterminacy by proposing a novel scissor-pair transformable solution.

The Library of Professor Meserve

Charles Francis Meserve was an early summer resident of Squirrel Island and an important educational reformer around the turn of the twentieth century. Charles married Fannie Philbrick, whose father, John W. Philbrick, built a house on Squirrel Island. Eventually, the Philbrick cottage passed to the Meserves and become home to their books

Curbing Tax Expenditures

Reviews trends in tax expenditures and their effects and examines three options for raising tax revenue by applying limits to large and widely utilized tax preferences: a fixed percentage credit, a cap based on income, and a constant percentage reduction

Learning to teach : the development of teaching knowledge in trained and untrained physical education teachers.

The primary purpose of this study was to further the understanding of how people learn to teach. The central research question focused on differences in teaching knowledge that may be associated with training and experience. Eight teachers were selected to participate in this study. They represented a wide range of teaching experience, formal training, professional certification and sport participation. The common criterion for selection was previous experience in the teaching of volleyball. Data were collected from both questionnaires and transcribed interviews which followed the viewing of a twenty-minute videotaped volleyball lesson. Results indicated differences among the participating teachers in content knowledge (the skills of playing volleyball), pedagogical knowledge (general teaching principles), and pedagogical content knowledge (content-specific teaching knowledge). The comments of trained teachers displayed a greater awareness of and concern for general teaching principles. In contrast, untrained teachers devoted most of their comments to lesson content. Experienced teachers, whether trained or untrained, demonstrated a superior understanding of the relationship between the nature of content and the needs of learners at different levels of skill development. In that regard, they had a more elaborately developed sense of pedagogical content knowledge. Untrained teachers cited their experience as students and athletes as major sources of information about teaching, while trained teachers pointed to experiences associated with their formal training. Members from both group indicated that they had learned from role models and early teaching experiences. Among trained and untrained teachers the sources for the differences in knowledge, and how that knowledge was processed, included the following: varied teaching contexts such as public high schools and university classes, the extent of teaching experience which ranged from one to eighteen years, and views about teaching that were influenced by previous experience in either coaching or teaching roles. Implications for teacher education and staff development include a need for training experiences that will integrate various forms of teaching knowledge. In addition, it is clear that teacher preparation programs must deal much more explicitly with the differences between coaching and teaching contexts

Modulating Intra-Nuclear LC3 with Small Molecules Rescues Cells from an Aneuploidogen-Induced Phenotype

Nuclear autophagy (nucleophagy) has been described as a cellular metabolic response by which nuclear material is actively degraded after stressors, such as nuclear damage or the onset of tumorigenesis. Here we describe nucleophagy as a process distinct from traditional macroautophagy in human cell lines. We found that although nuclear localization of LC3 is not dependent on particular nuclear importins, knockdown of nuclear importins (causing nuclear stress) can induce a nuclear autophagic response. Our characterization of nucleophagy was facilitated by chemical modulation of the process via two compounds discovered previously in a high content analysis. These small molecules bidirectionally regulate nuclear autophagy in human renal, pancreatic, and bladder cell lines. One molecule (NSC31762 or DTEP) enhances nuclear autophagic puncta and increases lysosomal targeting of LC3. Another molecule (NSC279895 or DIHI) reduces the nuclear localization of LC3. Finally, we applied these chemical tools in the setting of aneuploidy driven nuclear stress. The compound DIHI, shown to reduce nuclear autophagic puncta, was able to revert cells from aneuploidogen-induced phenotypes, possibly restoring homeostasis. These new tools will allow for a deeper exploration of nucleophagy, and could serve as proof-of-principle in guiding new therapies for diseases involving nuclear stress